The knowledge of the permittivity and its frequency behavior is important in both basic and applied research. The dielectric material properties are relevant for the design of radio-frequency and microwave devices, e.g. in mobile communication systems. Dielectric measurements can help control manufacturing processes. For example, changes in the viscosity and cure state of thermosetting resins can be monitored via changes in the dielectric properties of the material. The measurements can be made in actual processing environments such as presses, autoclaves, and ovens. In the agricultural sector the dielectric properties of food products can be used for the indirect determination of product quality factors such as moisture content, dry-matter content, and maturity. The dielectric measurement is a particularly informative technique for geophysical applications (see, for example, Calvert, T. J., Rau N. R., “Electromagnetic Propagation . . . A New Dimension in Logging”, SPE paper 6542, 1977). Nearly an order of magnitude separates the value of water dielectric constant from that of the other formation constituents. Thus, measurements of the effective formation permittivity are sensitive to the formation water content.
In the laboratory, dielectric properties can be measured by different methods employing various sample sizes and shapes (see, for example, H. E. Bussey, “Measurement of RF Properties of Materials. A Survey”, Proc. IEEE, vol. 55, pp. 1046-1053, 1967; Baker-Jarvis, J., Janezic, M. D., Riddle, B. F., Johnk, R., Kabos, P., Holloway, C. L., Geyer, R. G., Grosvenor, C. A., “Measuring the Permittivity and Permeability of Lossy Materials: Solids, Liquids, Metals, Building Materials, and Negative-index Materials”, NIST Technical Note 1536, 2004). The measurement technique depends on the frequency of interest. At frequencies up to several MHz a capacitive technique is typically employed. The material is placed in between the plates of a capacitor, and from the measurements of capacitance, the dielectric constant can be calculated. The capacitance model works well if the wavelength is much longer than the conductor separation.
However, for higher frequencies, especially in the GHz region, more sophisticated techniques need to be used, such as a transmission line or a microwave resonator. Transmission line methods are widely utilized because they allow for broadband measurements. In the past, coaxial transmission lines (also called “coaxial cells”) were commonly utilized. (See, for example, L. C. Shen, “A Laboratory Technique for Measuring Dielectric Properties of Core Samples at Ultra High Frequencies”, SPE paper 12552, 1983; W. B. Weir, “Automatic Measurement of Complex Dielectric Constant and Permeability at Microwave Frequencies”, Proc, IEEE, vol. 62, no. 1, pp. 33-36, 1974; R. N. Rau and R. P. Wharton, “Measurement of Core Electrical Parameters at UHF and Microwave Frequencies”, SPE 9380, 55th Annual Meeting of the SPE, Dallas, Tex., 1980).
The configuration of a prior art coaxial cell 100 containing a sample 105 is shown in the FIG. 1. A coaxial transmission line includes a center conductor 110 and an outer conductor 120. The sample 105 has the shape of a cylinder with the hole in the center, and is placed in between the outer and the inner electrodes in a section of the coaxial transmission line. The transmission and the reflection coefficients of the line can be related to the permillivity and the conductivity of the sample. The knowledge of both reflection and transmission coefficients (or, in the other words, the knowledge of all S-parameters of this line) allows for closed form expression derivation and simplifies the computation of permittivity and conductivity from experimental data. However, the coaxial lines require a coaxial sample that is placed, as shown, in the section of the line filling the space between the central and the outer conductors. In some cases, creating such a coaxial sample is easy, as with a liquid sample. In other cases, the inability to precisely shape the sample can limit the use of a coaxial cell. In the case of weakly consolidated materials, it is difficult to machine such a sample. This can be especially true for rock materials, such as coring samples, which usually must be ground into shape rather than using more conventional machining methods.
An improved cell, shown in FIG. 2, which has central conductor 210 and outer conductor 220, uses a cylindrically shaped sample 205 in an open section, and avoids the disadvantages of the common coaxial cell (see Taherian R., Habashy T., Yuen J., Kong J., “A Coaxial-Circular Waveguide for Dielectric Measurement”, IEEE Trans. Geoscience and Remote Sensing, vol. 29, No. 2, 321-330, 1991). In addition, the study of the cell response showed that it has the larger dynamic range and higher sensitivity than a conventional coaxial cell. As shown, the coaxial-circular cell of FIG. 2 includes two coaxial waveguides connected through to a central cylindrical section. In other words, the coaxial waveguides are abruptly truncated at the faces of the sample 205, which resides in a central cylindrical section and makes electrical contact with the central electrodes of coaxial waveguides. The sample has a simple cylindrical geometry without a hole in the center.
The full wave forward model predicting the response of the cell of FIG. 2 as a function of the sample length, permittivity and conductivity was developed and is presented in Taherian, Habashy, Yuen, and Kong, 1991, supra. In combination with an inversion algorithm, this model allows the determination of the permittivity and conductivity of the sample from the measured scattering parameters (S-parameters). The permittivity and conductivity estimate at a given frequency can be obtained from each measured S-parameter, and the inversion algorithm makes use of all four S-parameters for the improved accuracy and reliability of the measurement. To suppress the multiple reflection of waves between the connector's terminals and the coaxial-circular junction, two criteria have to be satisfied: The first is that all the TM modes that are reflected back towards the connector have to be evanescent (i.e. below cutoff). This is achieved by choosing the dimensions of the coax in such a way that the propagation constant of each reflected TM mode is an imaginary quantity. This causes the attenuation of the reflected TM modes as they propagate back towards the connector. The second design criterion is to ensure that the connector absorbs the entire reflected TEM mode and that nothing is reflected back at the connector. This is done by choosing the connector's impedance to be equal to the wave impedance of the TEM mode, which was 50Ω in the example.
An example measurement of the permittivity and conductivity of 1Ω-m brine is shown in FIGS. 3 and 4. FIG. 3 shows permittivity as a function of frequency, and FIG. 4 shows conductivity as a function of frequency. The measured values are compared with those predicted by the Klein-Swift model for the 1Ω-m brine. (See Klein, L. A., and Swift, C. T., “An Improved Model for the Dielectric Constant of Sea Water at Microwave Frequencies”, IEEE Trans. Antennas Propagt., vol. AP-25, pp. 104-111, 1977). It is evident from this comparison that measured dielectric data is in close agreement with the expected values.
It is among the objects of the invention to provide an improved apparatus for measuring properties, including complex dielectric permittivity, of samples as a function of frequency, with less restriction on the geometry and size of the sample than in prior art approaches.
It is also among the objects of the present invention to provide an improved connector for transition between coaxial waveguides of different diameters.